When we think about the building blocks of matter, we think about atoms. But in the 5th century B.C.E., one Greek philosopher had a different idea about the matter of matter. Plato believed the universe was made of earth, air, fire, water, and cosmos – each with a specific geometry. For Earth, it was the cube.

In the 1800s John Dalton came up with the first modern atomic model and Plato's conception of the cube became a memory. But now, remarkably, researchers say that he might have been on to something all along.

In a new paper, a team from the University of Pennsylvania (Penn), Budapest University of Technology and Economics, and University of Debrecen employed math, geology, and physics to show that the average shape of rocks on Earth is a cube.

"Plato is widely recognized as the first person to develop the concept of an atom, the idea that matter is composed of some indivisible component at the smallest scale," says Douglas Jerolmack, a geophysicist from Penn. "But that understanding was only conceptual; nothing about our modern understanding of atoms derives from what Plato told us."

"The interesting thing here is that what we find with rock, or earth, is that there is more than a conceptual lineage back to Plato," he adds. "It turns out that Plato's conception about the element earth being made up of cubes is, literally, the statistical average model for real earth. And that is just mind-blowing."

The research began when mathematician Gábor Domokos of the Budapest University of Technology and Economics, developed geometric models that predicted that natural rocks would fragment into cubic shapes.

Intrigued, Domokos consulted with two theoretical physicists – Ferenc Kun, an expert on fragmentation, and János Török, an expert on statistical and computational models. Realizing that this could be a substantial discovery, the researchers took their findings to Jerolmack to work together on the geophysical questions, as in: "How does nature let this happen?"

"When we took this to Doug, he said, 'This is either a mistake, or this is big,'" Domokos recalls. "We worked backward to understand the physics that results in these shapes."

"This paper is the result of three years of serious thinking and work, but it comes back to one core idea," says Domokos. "If you take a three-dimensional polyhedral shape, slice it randomly into two fragments and then slice these fragments again and again, you get a vast number of different polyhedral shapes. But in an average sense, the resulting shape of the fragments is a cube."

And not only did they find that cubes are what happen when our planet's rocks break into pieces – but this core mathematical pattern happens around the solar system as well, like on the mosaic-like surface of Jupiter's moon, Europa.

"Fragmentation is this ubiquitous process that is grinding down planetary materials," Jerolmack says. "The solar system is littered with ice and rocks that are ceaselessly smashing apart. This work gives us a signature of that process that we've never seen before."

Once the team had their mathematical models in place, they measured a wide variety of rocks – hundreds that they gathered for the study, and thousands more from previous research. And regardless of what the rocks had been subjected to – from natural erosion to dynamite – the researchers found the same cubic average.

So how did Plato come up with this several millennia ago?

One thing that helps to make sense of the discovery is to simplify it and consider that the parts that make solid objects need to fit together without any gaps. As it turns out, notes Penn, "the only one of the so-called platonic forms – polyhedra with sides of equal length – that fit together without gaps are cubes."

"Plato was very sensitive to geometry," Domokos says. "His intuitions, backed by his broad thinking about science, may have led him to this idea about cubes."

"One thing we've speculated in our group is that, quite possibly Plato looked at a rock outcrop and after processing or analyzing the image subconsciously in his mind," Jerolmack says. "He conjectured that the average shape is something like a cube."

And we're finally catching on, more than 2,400 years later.

The research was published in Proceedings of the National Academy of Sciences.